×

zbMATH — the first resource for mathematics

Numerical simulations of 2D potential flows in general relativity. (English) Zbl 0857.76048
Summary: Numerical solutions via the local characteristic approach have been obtained for the general-relativistic potential flow passing over a hard sphere and a black hole. These solutions have been used as a test of a two-dimensional code which extends some high-resolution shock-capturing methods, designed recently to solve nonlinear hyperbolic systems or conservation laws, to find the numerical solution of a wave equation in a multidimensional curved space-time.
MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
85-08 Computational methods for problems pertaining to astronomy and astrophysics
83-08 Computational methods for problems pertaining to relativity and gravitational theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abrahams, A.M.; Shapiro, S.L., Phys. rev. D, 41, 327, (1990)
[2] Colella, P.; Glaz, H.M., J. comput. phys., 59, 264, (1985)
[3] Colella, P.; Woodward, P.R., J. comput. phys., 54, 174, (1984)
[4] Einfeldt, B., SIAM J. num. anal., 25, 294, (1988)
[5] Harten, A.; Hyman, J.M.; Lax, P.D., Commun. pure appl. math., 29, 297, (1976)
[6] Harten, A.; Lax, P.D.; van Leer, B., SIAM rev., 25, 35, (1983)
[7] Fryxell, B.A.; Müller, E.; Arnett, W.D., ()
[8] Glaister, P., J. comput. phys., 74, 382, (1988)
[9] Lax, P., ()
[10] Lax, P.D.; Wendroff, B., Commun. pure appl. math., 13, 217, (1960)
[11] Martí, J.M., ()
[12] Martí, J.M.; Ibáñez, J.M.; Miralles, J.A., Phys. rev. D, 43, 3794, (1991)
[13] Petrich, L.I.; Shapiro, S.L.; Teukolsky, S.A., Phys. rev. lett., 60, 1781, (1988)
[14] Richtmyer, R.; Morton, K., Difference methods for initial-value problems, (1967), Interscience New York · Zbl 0155.47502
[15] Roe, P.L., J. comput. phys., 43, 357, (1981)
[16] Shu, C.W.; Osher, S.J., J. comput. phys., 83, 32, (1989)
[17] Van Leer, B., J. comput. phys., 23, 276, (1977)
[18] Van Leer, B., J. comput. phys., 32, 101, (1979)
[19] Van Leer, B., SIAM J. sci. stat. comput., 5, 1, (1984)
[20] Yee, H.C., VKI lecture notes in computational fluid dynamics, (1989), von Karman Institute for Fluid Dynamics Belgium
[21] Godunov, S.K., Mat. sb., 47, 271, (1959)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.